It’s a simple idea: You take a book; you leave a book. And it’s one that’s catching on all over the world through the organization Little Free Library, based in Hudson, Wis. Book lovers can send away for a small wooden structure and set it up so that passersby can take a book now and donate one later. Builders can register their library online at littlefreelibrary.org for various benefits.

Little Free Library suggests that each structure have a steward to watch over it, making sure it stays clean and filled with books. The Little Free Library website offers tips for stewards on such topics as what to do if the library is vandalized.

Todd Bol, the “first steward” and executive director of the organization, made the original little library in 2009 in memory of his mother, who was a teacher. He estimates there are now 20,000 such libraries officially registered worldwide. Many people find them charming.

“I’ve had plenty of times when I’ve installed [a Little Free Library] and people have hugged them,” Mr. Bol says. He’s heard a lot of heartwarming stories, too: One man told him that the book exchange had gotten his neighbors talking to one another again. A woman said that, on Halloween night, “the kids were paying more attention to the Little Free Library than the candy.”

Not everyone, however, has welcomed the little libraries. Earlier this summer, a Kansas boy who set up a Little Free Library in his front yard was told by the city of Leawood to take it down because it violated a city ordinance against structures in front yards. But when Spencer Collins appeared before the city council to make an appeal, the council excused his little library from the ordinance – at least until October.

“Saying ‘no’ to Little Free Library is like saying you’re going to stamp out a lemonade stand,” Bol said of the controversy. “The community doesn’t like it.”